1. Field of the Invention
This invention relates to quantum computing and to solid state devices that use superconducting materials to create and maintain coherent quantum states such as are required for quantum computing.
2. Description of Related Art
The field of quantum computing has generated interest in physical systems capable of performing quantum calculations. Such systems should allow the formation of well-controlled and confined quantum states. The superposition of these quantum states are then suitable for performing quantum computation. The difficulty is that microscopic quantum objects are typically very difficult to control and manipulate. Therefore, their integration into the complex circuits required for quantum computations is a difficult task.
Research on what is now called quantum computing traces back to Richard Feynman, [R. Feynman, Int. J. Theor. Phys., 21, 467-488 (1982)]. Feynman noted that quantum systems are inherently difficult to simulate with conventional computers but that observing the evolution of a quantum system could provide a much faster way to solve some computational problems.
Further efforts in quantum computing were initially concentrated on xe2x80x9csoftware developmentxe2x80x9d or building of the formal theory of quantum computing. Milestones in these efforts were the discoveries of the Shor and Grover algorithms. [See P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997); L. Grover, Proc. 28th STOC, 212-219 (1996); and A. Kitaev, LANL preprint quant-ph/9511026 (1995)]. In particular, the Shor algorithm permits a quantum computer to factorize natural numbers. The showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations of quantum computers. [See E. Knill, R. Laflamme, and W. Zurek, Science, 279, p. 342 (1998).]
One proposed application of a quantum computer is factoring of large numbers. In such an application, a quantum computer could render obsolete all existing encryption schemes that use the xe2x80x9cpublic keyxe2x80x9d method. In other applications, quantum computers (or even a smaller scale device, a quantum repeater) could allow absolutely safe communication channels where a message, in principle, cannot be intercepted without being destroyed in the process. [See H. J. Briegel et al., LANL preprint quant-ph/9803056 (1998) and the references therein.]
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among the N qubits, allowing the quantum states of the qubits to evolve under the influence of the entanglements, and reading the qubits after they have evolved. A qubit is conventionally a system having two degenerate quantum states, and the initial state of the qubit typically has non-zero probabilities of being found in either degenerate state. Thus, N qubits define an initial state that is a combination of 2N degenerate states. The entanglements control the evolution of the distinguishable quantum states and define calculations that the evolution of the quantum states performs. This evolution, in effect, performs 2N simultaneous calculations. Reading the qubits after evolution is complete determines the states of the qubits and the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses chemicals having degenerate spin states. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented the Shor algorithm for factoring of a natural number (15). However, efforts to expand such systems up to a commercially useful number of qubits face difficult challenges.
Another physical system for implementing a qubit includes a superconducting reservoir, a superconducting island, and a Josephson junction that can transmit a Cooper pair (of electrons) from the reservoir into the island. The island has two degenerate states. One state is electrically neutral, but the other state has an extra Cooper pair on the island. A problem with this system is that the charge of the island in the state having the extra Cooper pair causes long range electric interactions that interfere with the coherence of the state of the qubit. The electric interactions can force the island into a state that definitely has or lacks an extra Cooper pair. Accordingly, the electric interactions can end the evolution of the state before calculations are complete or qubits are read. This phenomenon is commonly referred to as collapsing the wavefunction, loss of coherence, or decoherence.
Another macroscopic alternative to microscopic quantum objects relies on superconducting line structures containing Josephson junctions. Superconductivity is a macroscopically coherent quantum phenomenon and therefore superconducting systems are attractive candidates for utilization in quantum computing circuits.
FIG. 1a shows an example of a Josephson junction 110 in a SQUID qubit 100. A Josephson junction refers to two superconducting electrodes separated by a thin tunnel barrier formed by a dielectric. FIG. 1a shows a SQUID (superconduction quantum interference device) qubit 100. Qubit 100 has a continous superconducting loop 101 with endpoints separated by a gap to form junction 110. Junction 110 is filled with a thin dielectric forming a potential barrier between the endpoints of line 101. A quantum superposition of magnetic flux states in the superconducting loop containing Josephson junction 101, qubit 100, is called macroscopic quantum coherence (MQC).
If an external magnetic field applied to qubit 100 provides a magnetic flux equal to one half the magnetic flux quantum, "PHgr"0/2, then the potential energy presented by the magnetic flux ("PHgr"int) states of qubit 100 has two symmetric minima as is shown in FIG. 1b. A magnetic flux trapped in qubit 100 can then tunnel between the two symmetric minima of the magnetic flux potential energy function. The degenerate ground states of a magnetic flux in qubit 100 are linear combinations of the states corresponding to the minima of the potential energy function (i.e. |0 greater than +|1 greater than  and |0 greater than xe2x88x92|1 greater than ). These degenerate states are split by the energy difference related to the tunneling matrix element. Therefore, if the coherence can be maintained long enough, the magnetic flux will quantum-mechanically oscillate back and forth between the two degenerate states.
The drawback of qubit 100 is that it is an open system and transition from one potential well to another is accompanied by the inversion of the magnetic field and superconducting screening currents surrounding qubit 100. The energy of this redistribution and the unknown external influences can be relatively large and can therefore cause decoherence (i.e., collapsing of the quantum mechanical wave functions). Moreover, the potential energy barrier, and therefore the energy split between the two degenerated states, cannot be controlled in situ, unless the Josephson junction is substituted by a small SQUID with independently-tunable critical current.
There is a continuing need for a structure for implementing a quantum computer. Further, there is a need for a structure having a sufficient number of qubits to perform useful calculations.
In accordance with the present invention, a qubit having a shaped long Josephson junction which can trap fluxons is presented. A qubit according to the present invention can offer a well-isolated system that allows independent control over the potential energy profile of a magnetic fluxon trapped on the qubit and dissipation of fluxons. Additionally, shaped long Josephson junctions can have shapes resulting in nearly any arbitrary desired potential energy function for a magnetic fluxon trapped on the junction.
Therefore, a superconducting qubit according to the present invention includes a long Josephson junction having a shape such as to produce a selected potential energy function indicating a plurality of pinning locations for a trapped fluxon in the presence of an externally applied magnetic field.
In one embodiment, the qubit has a heart-shaped long Josephson junction. The heart-shaped junction, in an external magnetic field applied in the plane of the Josephson junction and along a direction that the two lobes of the heart-shape are symmetric about (i.e., the symmetry axis of the heart), provides a spatially symmetric double-well potential energy function for pinning a trapped fluxon in one of the two lobes of the heart shape. The height of the potential barrier between the wells is controlled by the magnitude of the applied magnetic field. A non-symmetric double-welled potential energy function can be created by distorting the symmetry of the two lobes physically (i.e., distorting the xe2x80x9cheart-shapexe2x80x9d of the shaped Josephson junction). Additionally, the double-welled potential energy function can be altered in a controlled way by rotating the externally applied magnetic field in the plane of the Josephson junction and by applying a bias current.
A fluxon trapped on a heart-shaped junction will have a magnetic-field dependent potential energy function with minima on each of the two lobes, where the magnetic moment of the fluxon is aligned with the direction of the applied magnetic field in the plane of the junction. Pinning locations for fluxons are therefore created on each of the lobes of the heart-shaped junction. Fluxons can be trapped on the junction by applying a small bias current through the junction while the temperature of the superconductors forming the junction is lowered through the superconducting transition temperature. The potential energy function can then be controlled by rotating the magnetic field in the plane of the junction and by adjusting a small bias current through the junction. Additionally, the height of the potential well barrier between the two minima in the potential energy function is determined by the strength of the externally applied magnetic field.
In a second embodiment, a qubit having a spatially periodic potential well function is formed by a long Josephson junction shaped like a sine wave. When a magnetic field is applied in the plane of the sine-wave shaped junction, a periodic potential well function is formed. As before, the magnetic portion of the potential energy function is a minimum when the magnetic moment of the trapped fluxon traveling on the junction is aligned with the externally applied magnetic field in the plane of the junction and is a maximum when the magnetic moment has its maximum angle with the externally applied magnetic field. Pinning locations, therefore, are formed wherever the potential energy function is minimum. Again, variations of the potential energy function of a fluxon on the qubit can be altered by the bias current and the strength and direction of the externally applied magnetic field.
In a third embodiment, a qubit includes an S-shaped or M-shaped long Josephson junction. Again, the potential energy function of a trapped fluxon in the junction is a minimum where the angle between the magnetic moment of the fluxon and an externally applied magnetic field is a minimum.
The final state of a qubit according to the present invention can be determined by placing small, weakly coupled SQUID detectors in proximity to the pinning locations on the qubit. Alternatively, the final state of a qubit according to the present invention can be determined by measuring the escape current that, in general, is different for different pinning locations on the shaped long Josephson junction.
Entaglements can be formed between qubits made from long Josephson junctions by placing the Josephson junctions proximate one another so that a magnetic interaction between the magnetic moments of the fluxons can be established. Alternatively, a qubit with a periodic potential well can generate Bloch zones of a fluxon moving as a quantum particle in the periodic potential.
An array of qubits can be initialized by controlling the bias current through the junction and the magnetic field applied to the junction. The quantum state of the qubits will then evolve in a fashion predicted by the appropriate Hamiltonian, performing the requested quantum computation in the process. The result of the quantum computation can then be read-out by determining the location of the fluxon in each qubit of the array.
These and other embodiments are further discussed below with reference to the following figures.